Lesson 8: Multiplication as Scaling

Property

When a number $a$ is multiplied by a fractional scaling factor $f$:

• If $f < 1$, the product is smaller than $a$. ($a \times f < a$)
• If $f = 1$, the product is equal to $a$. ($a \times f = a$)
• If $f > 1$, the product is larger than $a$. ($a \times f > a$)

Examples

Property

To compare two products with a common factor, $a \times b$ and $a \times c$ (where $a > 0$), you only need to compare the scaling factors, $b$ and $c$.
The relationship between the products will be the same as the relationship between the scaling factors.

If $b > c$, then $a \times b > a \times c$.